Bounding Approaches for Generalization
Statisticians have recently developed propensity score methods to improve generalizations from randomized experiments that do not employ random sampling. However, these methods require strong and often controversial assumptions, which affect the validity and credibility of inferences. This article considers an alternative assumption, monotone sample selection, that partially identifies the population parameter, yielding a range of plausible values in place of a point estimate. We illustrate how this assumption bounds the parameter of interest and investigate the extent to which the bounds are informative. We also explore how the bounds can be tightened using stratification with propensity scores. We conduct a simulation study to examine the types of covariates that yield the largest precision gain. We apply the bounding approach to a completed cluster randomized trial on an educational technology aid.
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